This is a proposal to study feasibility of a spherical positron emission tomograph (S-PET). Extensive computer simulations of the S-PET predict that a spherical scanner would have increased spatial resolution and increased sensitivity far in excess of currently available machines. A spatial resolution of 3 mm is achievable, which makes the S-PET ideally suited for brain imaging. The increased sensitivity is derived from the large solid angle from which the radiation is collected. The sphere could be more than four times as sensitive as a corresponding cylindrical scanner. Although the spherical scanner could ultimately have 23 rings of detectors, we propose in this application to build a single ring with two opposing patches. A rotating phantom between the two patches can generate all the data needed for reconstruction from a sphere. For this proposal a cost-effective detector packing scheme is introduced. Also, a new megachannel coincidence circuit and a new sampling mode have been developed and will be used in the proposed scanner. A direct volume image reconstruction algorithm, previously developed, will be implemented in the proposed system.